"Public place" is indeed a vague term. In some statutes, it has a definition that includes publically accessible private property such as common areas of businesses, hospitals, etc. Does it include places where access depends on payment of a fee? How high above the ground do public places extend (thinking of photography drones)?

See also https://mentalhealthcop.wordpress.com/2013/09/20/place-to-wh... which shows the same ambiguity exists in the UK.